A star flash system angle of arrival estimation method based on factor graph message passing

Abstract

The application discloses a star flash system angle of arrival estimation method based on a factor graph message passing, comprising the following steps: S1, performing basic signal processing on a star flash receiving end received signal, obtaining channel information such as a star flash chip available received signal phase, amplitude and TDoA, and constructing a receiving array signal; S2, performing a variational angle of arrival estimation algorithm, a PDoA estimation algorithm and a TDoA estimation algorithm; S3, constructing a factor graph model of a joint estimation problem; S4, factor graph message passing iteration. The application effectively utilizes the advantages of a star flash system, such as super large bandwidth, super high clock synchronization accuracy and the like, to effectively suppress the influence of a multipath effect, significantly improves the angle of arrival estimation precision, and realizes tight coupling of several angle of arrival estimation algorithms based on spatial geometric constraints and a Bayesian factor graph model, effectively realizes low complexity effective fusion of estimation results of various algorithms, and enhances the precision and robustness of the star flash system angle of arrival estimation.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of integrated sensing and communication and Internet of Vehicles, and particularly relates to a star flash system angle of arrival estimation method based on factor graph message passing. BACKGROUND

[0002] In the field of modern wireless communication and sensing, the demand for high-precision spatial information acquisition is growing at an unprecedented rate. Integrated sensing and communication (ISAC) as the core evolution direction of 6G requires communication infrastructure to simultaneously consider high-speed data transmission and high-precision environmental sensing capabilities, enabling multi-dimensional information sensing of the distance, angle and even speed of surrounding objects, and providing key enabling for smart transportation, intelligent factories, low-altitude economy, etc. In the Internet of Vehicles (IoV) scenario, vehicles need to accurately know each other's position and direction angle information (V2V and V2I) to achieve high-reliability collaborative sensing.

[0003] Angle of Arrival (AoA) estimation technology plays a crucial role in such applications, as it analyzes the spatial incidence direction of the received signal to provide indispensable dimensional information for the precise positioning and behavior analysis of the target. Ultra Wide Band (UWB) technology has unique advantages and is a highly potential candidate for realizing high-precision angle of arrival estimation. UWB technology has excellent time resolution, which can accurately capture small signal propagation time differences; at the same time, UWB pulse signals have excellent multipath resolution and suppression capabilities, and perform more robustly than narrowband technology in complex indoor or urban environments. However, applying UWB technology to high-precision angle of arrival estimation also faces severe challenges: the core problem is to calculate the angle by accurately measuring the phase difference or time difference of signals between different antenna elements, which requires high precision of clock synchronization between different receiving channels in the array, resulting in increased system cost and power consumption, limiting the deployment potential of UWB angle of arrival estimation technology.

[0004] The recently emerging Near Link technology is widely considered to effectively solve the aforementioned problems. Natively designed to meet the demands of ultra-low latency and ultra-high reliability, Near Link's core breakthrough advantage lies in its ultra-high precision time synchronization capability, providing an unprecedented, extremely low-overhead foundation for precise synchronization across devices or within a single device channel. This native, robust clock synchronization mechanism can greatly simplify or even eliminate the need for complex external synchronization circuits or expensive clock sources in traditional UWB system angle-of-arrival estimation, thereby significantly reducing system hardware costs and complexity. Simultaneously, Near Link's powerful high-density connectivity naturally supports distributed deployment and multi-device collaborative sensing architectures, facilitating multi-node / multi-device collaborative angle-of-arrival measurement in integrated sensing or vehicle-to-everything (V2X) scenarios, further improving the spatial coverage and overall accuracy of angle-of-arrival estimation. Summary of the Invention

[0005] The purpose of this invention is to design a method for star-flash systems that integrates multiple angle-of-arrival estimation methods to achieve higher accuracy and robust posterior probability estimation of the angle of arrival.

[0006] The technical solution of this invention is as follows:

[0007] A method for estimating the angle of arrival (ADO) of a star-bomb system based on factor graph messaging, which integrates variational ADO estimation, PDoA estimation, and TDoA estimation algorithms, specifically includes the following steps:

[0008] S1. For the star flash receiver, integrate the IQ channel received signals, perform signal processing on the received signals, obtain the phase, amplitude and TDoA channel information of the received signals provided by the star flash chip, and construct the received array signal to facilitate subsequent signal processing.

[0009] S2. Execute the variational angle-of-arrival (AOA) estimation algorithm, the PDoA estimation algorithm, and the TDoA estimation algorithm. Specifically, for the variational AOA estimation algorithm, the estimation problem is reorganized into a line spectrum estimation paradigm. A variational Bayesian framework is constructed to obtain the variational lower bound of the variational problem. Maximizing the variational lower bound is used as the optimization objective to estimate the posterior probabilities of channel parameters such as the angle of arrival, and the posterior probability of the angle of arrival is expressed in the form of a von Mises distribution. For the PDoA estimation algorithm, the average differential phase difference of the antennas is calculated for the received array signal, thereby achieving point estimation of the angle of arrival. For the TDoA estimation algorithm, the average TDoA between antennas is calculated from the output of step S1, eliminating random clock error interference, thereby achieving point estimation of the angle of arrival.

[0010] S3. Describe the geometric constraint model between channel variables based on the geometric wireless channel model, and thus construct a factor graph model for the joint estimation problem.

[0011] S4, factor graph message passing iteration; calculating the Bayes messages passing between each factor node and variable node based on the factor graph structure, updating the probability estimation of each variable gradually through the message iteration between each factor node and variable node, realizing the message fusion of multiple estimation methods, until all the Bayes messages converge, and outputting the posterior probability estimation result of the angle of arrival.

[0012] Beneficial effects

[0013] The super large bandwidth and super high clock synchronization precision of the star flash system are effectively utilized to effectively suppress the influence of multipath and significantly improve the angle of arrival estimation precision; the variational Bayes framework is utilized to realize low-complexity variational angle of arrival estimation, and the estimation result of the angle of arrival is output in the form of an easy-to-handle Von Mises distribution, facilitating subsequent application and being more robust; the spatial geometric constraint and the Bayes factor graph model are utilized to realize the close coupling of several angle of arrival estimation algorithms, effectively utilize the advantages of multiple dimensional resources such as space and time to realize the effective fusion of the estimation results of multiple algorithms, and enhance the precision and robustness of the angle of arrival estimation of the star flash system. A reliable angle of arrival estimation scheme is provided for the integration of sensing and feeling, the Internet of Vehicles scene and the like. BRIEF DESCRIPTION OF DRAWINGS

[0014] Figure 1 It is a total flowchart of the angle of arrival estimation of the star flash system of the application;

[0015] Figure 2 It is a practical test scene diagram of the embodiment of the application;

[0016] Figure 3 It is a factor graph model described in the embodiment of the application;

[0017] Figure 4 It is a comparison diagram of the estimation performance of the method proposed in the embodiment of the application;

[0018] Figure 5 It is a comparison diagram of the running time of the method proposed in the embodiment of the application. DETAILED DESCRIPTION

[0019] The following describes the embodiments of the application by specific specific embodiments, but is not intended to limit the exemplary embodiments according to the application. In order to avoid confusion or obscure the focus of the application, some specific details will be omitted in the description. It should be noted that the embodiments in the application and the features in the embodiments can be combined with each other without conflict. In order to make the purpose, technical scheme and advantages of the application more clear, the embodiments of the application will be further described in detail below with reference to the drawings.

[0020] A star flash system angle of arrival estimation method based on factor graph message passing, comprising the following steps: (as Figure 1 )

[0021] S1, star flash receiving end signal collection and processing;

[0022] For the star flash receiving end, integrate the IQ route receiving signal, calculate the complex form of the receiving signal of each antenna, and combine the peak value monitoring algorithm to find the maximum amplitude of the impulse signal point of each antenna by calculating the signal amplitude. Arrange the impulse signal of each antenna in order to form a receiving signal complex matrix . And rely on the ultra-high precision clock synchronization capability of the star flash system to obtain the time difference of arrival (TDoA) between antennas.

[0023] S2, variation angle of arrival estimation algorithm, PDoA estimation algorithm and TDoA estimation algorithm;

[0024] In the above scenario, the receiving signal matrix of the star flash receiving end constructed in S1 , can be modeled as:

[0025]

[0026] where, is the channel gain complex coefficient, is a two-dimensional steering matrix, and are the cosine values of the angles of arrival along the x-axis and y-axis directions of the receiving antenna array, respectively. is an additive white Gaussian noise matrix, is the noise power.

[0027] For a two-dimensional surface array, the steering matrix can be decomposed into the Kronecker product of steering vectors along the x-axis and y-axis directions of the surface array:

[0028]

[0029]

[0030] where, the vector represents the receiving steering vector when the antenna spacing is half a wavelength, is the number of antennas, is the Kronecker product operator. From the above calculation relationship, the two angle of arrival estimation problems of and can be decomposed into the angle of arrival estimation problems along the x-axis and y-axis directions of the receiving antenna array. At this time, is combined and expressed as , for the receiving signal matrix , if it is decomposed into a single-dimensional receiving signal vector along the x-axis or y-axis direction, The estimation problem of the arrival angle is only related to the estimation of the channel complex gain coefficient and the corresponding single direction (x-axis or y-axis) arrival angle, and the problem is considered as a standard linear spectrum estimation problem.

[0031] Taking the x-axis direction as an example, if the received signal matrix is taken along the x-axis direction, a received signal vector is taken along the x-axis direction, the relationship between the arrival angle along the x-axis can be expressed as:

[0032]

[0033] wherein, is the channel gain complex coefficient of the x-axis direction, is an additive Gaussian white noise vector.

[0034] Similarly, for the y-axis direction, if the received signal matrix is taken along the y-axis direction, a received signal vector is taken along the y-axis direction, the relationship between the arrival angle along the y-axis can be expressed as:

[0035]

[0036] wherein, is the channel gain complex coefficient of the y-axis direction, is an additive Gaussian white noise vector.

[0037] The present application abstracts the arrival angle estimation problem into a linear spectrum estimation problem, and then uses the variational arrival angle estimation algorithm, the PDoA estimation algorithm and the TDoA estimation algorithm to complete the above parameter estimation.

[0038] (1) Variational arrival angle estimation algorithm

[0039] Different from the traditional gridding estimation method, the variational arrival angle estimation algorithm uses a non-gridding parameter estimation method to realize the continuous value estimation in the angle domain.

[0040] For the above linear spectrum estimation problem, according to the received signal expression form and the additive Gaussian white noise form, the likelihood probability of the received signal can be expressed as a complex Gaussian distribution:

[0041]

[0042] wherein, is or , is or , For or .

[0043] According to Bayesian probability analysis, the posterior probability of the angle of arrival and the complex coefficient of channel gain can be expressed as:

[0044]

[0045] where the joint probability distribution of the problem to be estimated can be expressed as:

[0046]

[0047] The angle of arrival and the complex coefficient of channel gain can be estimated by means of Bayesian inference, but the calculation process thereof depends on high complexity integration. Therefore, the present application relies on variational inference to estimate a variational probability to approximate the posterior probability of the angle of arrival in a low complexity calculation manner. The core calculation process of the angle of arrival estimation by means of variational inference can be converted into maximizing the variational lower bound (ELOB) of the Bayesian estimation model, and under the goal of maximizing the ELOB, the posterior probability of the angle of arrival after the variation can be calculated as:

[0048]

[0049] wherein represents taking the real part, is the prior probability of , and the variational calculation parameter is calculated as:

[0050]

[0051] wherein is the conjugate of the estimated value of . In each round of iteration process, the estimated values of and can be sequentially iteratively calculated based on the results of the last round of iteration according to the following formula:

[0052]

[0053]

[0054]

[0055] ​

[0056] The von Mises distribution is a normal distribution on a circle. In this invention, it is used to describe the posterior distribution of the angle of arrival, and its probability density function is expressed as follows:

[0057]

[0058] Among them, parameters and These are the average direction and concentration parameters, respectively. It is a class of p-order modified Bessel functions.

[0059] make Then the above formula can be rewritten as:

[0060]

[0061] The posterior probability of the angle of arrival Approximately represented by the von Mises distribution:

[0062]

[0063] Among its parameters and The following methods were used to calculate the results:

[0064] Step 1: Initialization ,

[0065] in Indicates taking a vector The Phase angle of the term, vector .

[0066] ,in and These are the two parameters of the prior distribution.

[0067] Let vector and All The vector, and its first... Each element can be calculated as: , , where the function .

[0068] Step 2: Loop through ,calculate ,in This represents the rounding function.

[0069] Step 3: find the index of the largest magnitude in the vector and determine the corresponding angle estimate , define the function ,

[0070] Take Newton method to refine the estimate, define the first and second derivatives of the function , if , the function is locally concave, output ; otherwise, output , .

[0071] So far, the posterior probability of the angle of arrival can be expressed in the form of von Mises distribution.

[0072] Repeat the calculation of the estimates of all variables above until all estimates converge, and output as the posterior probability distribution of the angle of arrival.

[0073] Unlike traditional point estimates, this method performs complete Bayesian processing by calculating the posterior probability density function of the angle of arrival, and fully considers the uncertainty of the angle of arrival estimate. The von Mises distribution is used to approximate the posterior probability of the angle of arrival. The introduction of this uncertainty improves the performance of the entire Bayesian inference.

[0074] The variational angle of arrival estimation algorithm relies on the spatial domain resources of the antenna array to estimate the angle of arrival. Compared with the PDoA estimation algorithm, it has better estimation performance and realizes soft estimation of the angle of arrival, but the computational complexity is , which is relatively high compared with the PDoA estimation algorithm.

[0075] (2) PDoA estimation algorithm

[0076] For the received signal matrix , it is decomposed into a single-dimensional received signal vector ( or ) along the x-axis or y-axis direction. The phase difference between adjacent elements of the received vector ( or ) is calculated item by item to form the PDoA vector , then the angle of arrival along the x-axis direction or the y-axis direction The calculation formula is:

[0077] ,

[0078] ​The PDoA estimation method directly performs arrival angle estimation based on a complex signal phase formed by IQ channel signals output by the star flash, has extremely low calculation complexity, but is susceptible to phase noise interference, and has relatively low estimation accuracy compared with the variational arrival angle estimation method.

[0079] (3) TDoA estimation method

[0080] Along the x-axis or y-axis direction, TDoA information output by a star flash receiving end is acquired to form a TDoA vector Then, the arrival angle (along the x-axis direction or the y-axis direction) can be calculated as:

[0081] ,

[0082] Among them, is the system operating frequency. The TDoA estimation method directly relies on the ultra-wide bandwidth resource and high-precision time resolution advantage of the star flash system to realize accurate estimation of the arrival angle, and compared with the variational arrival angle estimation method and the PDoA estimation method, a new dimension advantage is introduced.

[0083] S3, factor graph model construction

[0084] According to the geometric constraint model between the channel variables described by the geometric wireless channel model, it can be seen that the angles obtained by the several arrival angle estimation methods in S2 all satisfy the spatial geometric constraint of the same transceiver position. In order to realize the close coupling of the three estimation methods, the corresponding factor graph model is constructed in this embodiment:

[0085] The received signals to be processed in the x-axis and y-axis directions of the variational arrival angle estimation method, the PDoA estimation method and the TDoA estimation method are represented as: , , , , , (Subscripts 1, 2 and 3 represent the received signals processed by the variational arrival angle estimation method, the PDoA estimation method and the TDoA estimation method respectively, and subscripts x and y represent the received signal vectors decomposed along the x-axis and the y-axis respectively);

[0086] The estimated arrival angles are represented as: , , , , , (Subscripts 1, 2 and 3 represent the angles estimated by the variational arrival angle estimation method, the PDoA estimation method and the TDoA estimation method respectively, and subscripts x and y represent the arrival angles along the x-axis and the y-axis respectively);

[0087] with joint estimated angle of arrival value and are connected variable nodes, which are connected with , , , , , between the factor nodes are denoted as: , , , , , ;

[0088] According to the above-mentioned construction factor graph model as shown in Figure 3 , wherein the hollow circle represents the variable node, the solid square represents the factor node, and the estimated results of the three methods are realized by the actual channel AoA parameters and achieve close coupling.

[0089] S4, factor graph message passing iteration;

[0090] The present application updates the variable probability based on the message passing criterion, and relies on the message approximation to greatly reduce the computational complexity. The following is the calculation process of the Bayesian message in the factor graph, denotes the Bayesian message passing from node a to node b, where the variable angle of arrival estimation algorithm is taken as an example.

[0091] For the Bayesian message between the variable node and the factor node , it can be calculated as:

[0092]

[0093] wherein, is the prior information of the corresponding angle of arrival, in order to facilitate the subsequent Bayesian message calculation, the prior information is represented as Von Mises distribution:

[0094]

[0095] wherein, takes the equal-weighted average sum of the parameters and , takes the smaller value of the parameters and .

[0096] ​​​The variational DOA estimation algorithm described in S2 can be expressed as a von Mises distribution:

[0097]

[0098] The Bayesian message can be expressed as a von Mises distribution:

[0099]

[0100]

[0101] For and the other two algorithms, the message passing calculation is consistent with the variational DOA estimation algorithm estimation , only the difference in the notation. The Bayesian message calculation process of the PDoA estimation algorithm and the TDoA estimation algorithm is listed as follows, and the calculation principle is completely consistent with the Bayesian message calculation principle of the variational DOA estimation algorithm described above.

[0102] Take the PDoA estimation algorithm estimation as an example:

[0103]

[0104]

[0105] Wherein the value of the DOA estimated by the PDoA estimation algorithm described in S2 is multiplied by :

[0106]

[0107]

[0108] Wherein, take the equal-weighted average of the parameters and , and . take the smaller value of the parameters and .

[0109]

[0110]

[0111] The PDoA estimation algorithm estimates and the estimation method is consistent, only the difference in the notation.

[0112] estimated by the TDoA estimation algorithm For example:

[0113]

[0114]

[0115] wherein the value of is the angle of arrival estimated by the TDoA estimation algorithm in S2 multiplied by :

[0116]

[0117] wherein,

[0118] take the average of the parameters and with equal weights, take the smaller value of the parameters and .

[0119]

[0120]

[0121] estimated by the TDoA estimation algorithm is consistent with the method of estimating , only the difference in the label.

[0122] It should be noted that, since the PDoA estimation algorithm and the TDoA estimation algorithm directly output the point estimate of the angle of arrival, it is reasonably scaled here to the parameter , which takes the value of the von Mises distribution. The probability density function of this distribution behaves as an approximate impulse function. The specific scaling method is: taking the point estimate as the parameter of the von Mises distribution , select a large value as the parameter , which reflects the uncertainty of the angle of arrival estimation. The larger the value, the smaller the uncertainty. In the experimental part, we take , construct the von Mises distribution as the posterior probability of the angle of arrival estimated by the two methods. The posterior probability output by the variational angle of arrival estimation algorithm is updated with each iteration of the factor graph; the posterior probability output by the PDoA estimation algorithm and the TDoA estimation algorithm is not updated with each iteration of the factor graph, but the rest of the message passing method is consistent with the variational angle of arrival estimation algorithm.

[0123] ​​​The above Bayesian message is updated by cyclic iteration, and the specific process is as follows: on the basis of the Bayesian message of the last round of iteration, the new Bayesian message between the adjacent factor nodes and variable nodes is recalculated in turn until the bidirectional Bayesian message between all factor nodes and variable nodes in the graph is updated, and then the iteration process is considered to be completed.

[0124] If all the Bayesian messages of a round of update change less than a certain pre-set threshold compared with the last round, or the iteration number reaches a pre-set upper limit of the iteration number, the iteration is stopped, and the estimation result is output. In order to avoid complex marginal integration, and considering the real-time update of the posterior probability output by the variational angle of arrival estimation algorithm, the following is taken: and The posterior probability distribution of the final output and The output result is a von Mises distribution, which is convenient for subsequent positioning and the like.

[0125] Figure 1 The above is the overall flowchart of the factor graph message passing-based star flash system angle of arrival estimation, which covers all steps from S1 to S4.

[0126] Figure 2 The above is an actual test scene diagram.

[0127] Figure 3 The above is the factor graph model, in which the white circle represents a variable node, and the black square represents a factor node.

[0128] Figure 4 The above is the estimation performance comparison diagram of the method, and it can be seen that on the basis of the variational angle of arrival estimation algorithm, the PDoA estimation algorithm and the TDoA estimation algorithm are fused into the factor graph, which can effectively improve the angle of arrival estimation accuracy, especially in the case of medium and low signal-to-noise ratio.

[0129] Figure 5 The above is the running time comparison diagram of the method, and it can be seen that when more algorithms are fused into the factor graph, the algorithm running time is longer, but it is always shorter than the running time of the variational angle of arrival estimation algorithm, because the convergence speed of the variational angle of arrival estimation algorithm is slow in the absence of priori.

[0130] The above is only a specific embodiment of the present application, and it should be pointed out that for ordinary skilled persons in the technical field, the specific implementation of the present application cannot be limited to these descriptions, and any modification, equivalent replacement, improvement and the like made within the spirit and principles of the present application should be included in the protection scope of the present application. Those skilled in the art can make various changes in form and details, including making a number of simple deductions or replacements, without departing from the spirit and scope of the present application.

Claims

1. A method for estimating the angle of arrival (AOA) of a star-flash system based on factor graph message passing, characterized in that, Includes the following steps: S1. For the star flash receiver, integrate the IQ channel received signals, perform signal processing on the received signals, obtain the phase, amplitude and TDoA channel information of the received signals provided by the star flash chip, and construct the received array signal to facilitate subsequent signal processing. S2. Execute the variational angle of arrival estimation algorithm, PDoA estimation algorithm, and TDoA estimation algorithm; For the variational angle of arrival estimation algorithm, the estimation problem is organized into a line spectrum estimation paradigm. A variational Bayesian framework is constructed to obtain the variational lower bound of the variational problem. The posterior probability of the angle of arrival channel parameters is estimated with the optimization objective of maximizing the variational lower bound. The posterior probability of the angle of arrival is expressed in the form of a von Mises distribution. For the PDoA estimation algorithm, the average differential phase difference of the antenna is calculated for the received array signal, thereby realizing the point estimation of the angle of arrival; For the TDoA estimation algorithm, the average TDoA between antennas is calculated from the output of step S1, eliminating random clock error interference, thereby achieving point estimation of the angle of arrival; S3. Describe the geometric constraint model between channel variables based on the geometric wireless channel model, and then construct the factor graph model of the joint estimation problem; S4. Factor graph message passing iteration: Based on the factor graph structure, calculate the Bayesian messages passed between each factor node and variable node. Through message iteration between each factor node and variable node, gradually update the probability estimates of each variable, realize message fusion of multiple estimation methods, until all Bayesian messages converge, and output the posterior probability estimate of the angle of arrival. In step S2, the variational angle of arrival estimation algorithm is specifically as follows: Received signal matrix of the star flash receiver Based on geometric channel modeling: in, These are the complex coefficients of the channel gain. It is a two-dimensional guiding matrix. and These are the cosine values ​​of the angle of arrival along the x-axis and y-axis of the receiving antenna array, respectively. The matrix is ​​an additive white Gaussian noise matrix. Noise power; For a two-dimensional array, the guiding matrix is ​​decomposed into the Kronecker product of guiding vectors along the x-axis and y-axis of the array: Where, vector This represents the receive steering vector when the antenna spacing is half a wavelength. For the number of antennas, This is the Kronecker product operator; The angle of arrival estimation problem can be simplified into a line spectrum estimation problem, as follows: In the x-axis direction, the received signal matrix Take a received signal vector along the x-axis direction , With the angle of arrival along the x-axis The relationship is represented as: in, These are the complex coefficients of the channel gain in the x-axis direction. It is an additive white Gaussian noise vector; The y-axis direction will receive the signal matrix. Take a received signal vector along the y-axis direction , With the angle of arrival along the y-axis The relationship is represented as: in, These are the complex coefficients of the channel gain in the y-axis direction. It is an additive white Gaussian noise vector; Then, the variational angle of arrival estimation algorithm is used to solve the above line spectrum estimation problem; The variational angle of arrival estimation algorithm calculates the line spectrum estimation problem as follows: Based on the form of the received signal and the form of additive white Gaussian noise, the likelihood probability of this received signal is... Represented as a complex Gaussian distribution: in, for or , for or , for or ; According to Bayesian probability analysis, for the angle of arrival of the parameter to be estimated... and channel gain complex coefficients posterior probability Represented as: The joint probability distribution of the problem to be estimated Represented as: The core computational process for angle-of-arrival estimation using variational inference is transformed into maximizing the variational lower bound (ELOB) of the Bayesian estimation model. Under the objective of maximizing this ELOB, the posterior probability of the variationally derived angle of arrival is... Calculated as: in, Indicates taking the real part, for The prior probability is calculated based on the variational parameters. The calculation is as follows: in, for The conjugate of the estimated value; in each iteration... and The estimated value is based on the results of the previous iteration and is calculated iteratively using the following formulas in sequence: The von Mises distribution is a normal distribution on a circle, used to describe the posterior distribution of the angle of arrival. Its probability density function is expressed as follows: Among them, parameters and These are the average direction and concentration parameters, respectively. It is a class of p-order modified Bessel functions; make Then the above formula can be rewritten as: The posterior probability of the angle of arrival Represented as a von Mises distribution: Among its parameters and The following methods were used to calculate the results: Step 1: Initialization , in Indicates taking a vector The Phase angle of the term, vector ; ,in and These are the two parameters of the prior distribution; Let vector and All The vector, and its first... Each element is calculated as follows: , , where the function ; Step 2: Looping through ,calculate ,in This represents the rounding function; Step 3: Find The index of the vector with the largest magnitude And determine the corresponding angle estimate. Define function , The estimation results are refined using Newton's method, and a function is defined. First derivative and second derivative , ,if Explain the function It is locally concave, output Otherwise, output , ; Thus, the posterior probability of the angle of arrival is expressed as a von Mises distribution; Repeat the above estimation calculations for all variables until all estimation results converge, then output the results. As the posterior probability distribution of the angle of arrival.

2. The method for estimating the angle of arrival of a star-flash system based on factor graph message passing according to claim 1, characterized in that, Step S1 specifically involves: for the star flash receiver, integrating the IQ channel received signals, calculating the complex form of the received signal of each antenna, and combining it with the peak monitoring algorithm to find the impulse signal point with the largest amplitude of each antenna by calculating the signal amplitude. The impulse signals from each antenna are arranged sequentially into a complex matrix of received signals. Furthermore, relying on the ultra-high precision clock synchronization capability of the star flash system, the arrival time difference between antennas is obtained.

3. The method for estimating the angle of arrival of a starburst system based on factor graph message passing according to claim 1, characterized in that, In step S2, the PDoA estimation algorithm is specifically as follows: For the received signal matrix Decomposed into a single-dimensional received signal vector along the x-axis or y-axis direction. Right now or Calculate the received vector item by item Right now or The phase difference between two adjacent elements constitutes the PDoA vector. Then the angle of arrival along the x-axis or y-axis direction The calculation formula is: 。 4. The method for estimating the angle of arrival of a star-flash system based on factor graph message passing according to claim 1, characterized in that, In step S2, the TDoA estimation algorithm is specifically as follows: Along the x-axis or y-axis, obtain the TDoA information output from the star flash receiver to construct the TDoA vector. The angle of arrival is then calculated as follows: in, This refers to the system's operating frequency.

5. The method for estimating the angle of arrival of a star-flash system based on factor graph message passing according to claim 1, characterized in that, In step S3, the factor graph model is as follows: The variational angle-of-arrival estimation algorithm, PDoA estimation algorithm, and TDoA estimation algorithm are combined in... and The received signal to be processed in the axial direction is represented as follows: , , , , , The subscripts 1, 2, and 3 represent the received signals processed by the variational angle of arrival estimation algorithm, the PDoA estimation algorithm, and the TDoA estimation algorithm, respectively, and the subscripts x and y represent the received signal vectors obtained by decomposition along the x and y axes, respectively. The estimated angle of arrival is expressed as follows: , , , , , The subscripts 1, 2, and 3 represent the angles estimated by the variational angle of arrival estimation algorithm, the PDoA estimation algorithm, and the TDoA estimation algorithm, respectively, and the subscripts x and y represent the angles of arrival along the x and y axes, respectively. Jointly estimate the angle of arrival and To connect variable nodes, they are... , , , , , The factor nodes between them are denoted as: , , , , , ; The estimation results of the three methods—variational angle of arrival (ADO) estimation algorithm, PDoA estimation algorithm, and TDoA estimation algorithm—are compared with the actual channel angle of arrival parameters. and Achieve tight coupling.

6. The method for estimating the angle of arrival of a starburst system based on factor graph message passing according to claim 1, characterized in that, In step S4, the calculation process of the Bayesian message in the factor graph is as follows, where This represents a Bayesian message transmitted from node a to node b: Variational Angle of Arrival Estimation Algorithm as follows: For variable nodes With factor nodes The Bayesian message between them is calculated as follows: in, To correspond to the prior information on the angle of arrival, and to facilitate subsequent Bayesian message calculation, this prior information is represented as a von Mises distribution: in, Pick and parameters and Equal weighted summation average, Get parameters and The smaller value; The variational angle-of-arrival estimation algorithm described in S2 is represented by a von Mises distribution: Then Bayesian information It can be represented as a von Mises distribution: for And the other two algorithms, whose message passing computation and variational angle of arrival estimation algorithms estimate... They are the same, differing only in their labels; PDoA estimation algorithm estimates The method is as follows: in The value is the angle of arrival estimated by the PDoA estimation algorithm described in S2 multiplied by : in, Pick and parameters and Equal weighted summation average, Get parameters and The smaller value; TDoA estimation algorithm estimates The method is as follows: in The value is the angle of arrival estimated by the TDoA estimation algorithm described in S2 multiplied by : in, Pick and parameters and Equal weighted summation average, Get parameters and The smaller value; estimate With estimation The methods are the same, only the labels are different; The Bayesian messages are iteratively updated in the following way: Based on the Bayesian messages of the previous iteration, new Bayesian messages between adjacent factor nodes and variable nodes are recalculated in turn until all bidirectional Bayesian messages between factor nodes and variable nodes in the graph are updated, which is considered the end of one iteration process. If the changes in all Bayesian messages in a certain round of updates are less than a certain preset threshold compared to the previous round, or if the number of iterations reaches the preset maximum number of iterations, then the iteration is stopped and the estimation result is output. To avoid complex edge integrals, and considering the real-time update of the posterior probability output by the variational angle of arrival estimation algorithm, we take... and For the final output and The posterior probability distribution.

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